©2020 Compass Learning Technologies → Live Mathematics on the Web → Geometry Expressions Showcase → Meeting a Friend

 

Meeting a Friend

Saltire Software, home of Geometry Expressions and GXWeb

Download a Geometry Expressions Model for Meeting a Friend

GXWeb Meeting with a Friend Model (drag point E and explore!)

Symbolic computations on this page use Nerdamer Symbolic JavaScript to complement the in-built CAS of GXWeb

Learn How: Create Your Own GXWeb Tasks (like this one!)

 

Adapted from New South Wales Higher School Certificate 2005 Mathematics examination, Question 10 (copyright held by NSW Board of Studies).

 

Two friends agree to meet during their lunch hour, but both are very busy and unsure whether they can make it.

They each agree to wait for '\(x\)' minutes and, if the other has not arrived, to leave.

What is their chance of meeting? Drag the WaitTime point to explore this problem.

 

---

Let the unit square describe their lunch hour, and each point \((x, y)\) within that square represent each of our times of arriving.

Then the point (1/2, 2/3) would indicate that I arrived at 12:30, and my friend arrived at 12:40.

How then do the inequalities \(x - y <= t\) and \(y - x <= t\) describe our chance of meeting?

Points which lie within the shaded hexagon correspond to times of arrival for which we would meet. Points outside the polygon are times for which we would not meet. In fact, our chance of meeting for any wait time, \(x\), will correspond to the AREA of the shaded figure - and the moving point on the screen has coordinates \((x, area(x))\).

What is the algebraic model that best fits this situation? More simply, what is the formula for the area of the hexagon for any wait time, \(x\)?

Try building your own model for this problem using GXWeb and use it to explore both the geometry and the algebra involved.

 

---

About the MathBoxes...

Hint: When entering mathematical expressions in the math boxes below (f(x), g(x), h(x) and the assessment questions), use the space key to step out of fractions, powers, etc. On Android, begin entry by pressing Enter.

Type simple mathematical expressions and equations as you would normally enter these: for example, "x^2[space]-4x+3", and "2/3[space]". For more interesting elements, use Latex notation (prefix commands such as "sqrt" and "nthroot3" with a backslash (\)): for example: "\sqrt(2)[space][space]". More?

 

Jump to Top

Jump to Assessment

Jump to GXWeb